(1+cosA+sinA)/(1+cosA-sinA)=(1+sinA)/cosA

Dhanalakshmi · June 29, 2019, 6:20am

Dhanalakshmi · June 29, 2019, 6:22am

LHS = (1+cosA+sinA)/(1+cosA-sinA)
= (1+cosA+sinA)(1+cosA+sinA)/(1+cosA-sinA)(1+cosA+sinA)
= (1+cosA+sinA)²/(1+cosA)² -sin2A
= 1+cos²A+sin²A+2cosA+2sinA+2sinAcosA/(1+cos²A+2cosA)-sin²A
= 2+2cosA+2sinA+2sinAcosA/2cos²A+2cosA
= (1+cosA)+sinA(1+cosA)/cosA(cosA+1)
= (1+cosA)(1+sinA)/cosA(cosA+1)
= 1+sinA/cosA
= RHS